In court on Tuesday, Van der Zwaan was also fined $20,000 and sentenced to two months of supervised release.

Who is Van der Zwaan?

The Dutchman is a London-based lawyer who formerly worked at international law firm Skadden, Arps, Slate, Meagher & Flom.

The firm, which is co-operating with the investigation and which fired him last year, worked with former Trump campaign chief Paul Manafort and his ex-colleague Mr Gates at a time when they were both political consultants in Ukraine.

Van der Zwaan, who speaks French and Russian and graduated from King’s College London in 2006, is married to the daughter of Russian billionaire German Khan.

“What I did was wrong. I apologise to this court, and I apologise to my wife,” he said at the hearing.

What were the accusations?

According to court documents, Van der Zwaan “wilfully and knowingly” made false statements to investigators while answering questions about a report prepared in 2012 by his former law firm for the Ukrainian Ministry of Justice on the trial of Yulia Tymoshenko.

Ms Tymoshenko, a former Ukrainian prime minister, was jailed in 2011 over a gas deal with Russia, in charges she said were politically motivated.

The report prepared by Skadden was used to defend Ukraine’s then pro-Russia President Viktor Yanukovych from international criticism over the jailing of Ms Tymoshenko, a bitter rival who he defeated to become president in 2010.

Mr Mueller’s indictment said Van der Zwaan “deleted and otherwise did not produce emails sought by the special counsel’s office” and made a false statement about when he was last in contact with Mr Gates and “Person A”, who has not been identified but is described as a long-term business associate of Mr Gates and Mr Manafort.

Mr Gates and Mr Manafort have been hit with a number of charges, including conspiracy to launder money and acting as “unregistered agents” of Mr Yanukovych and his party.

Mr Manafort has denied all charges against him. Mr Gates has admitted conspiracy and lying to investigators in a plea deal.

A milestone – but Manafort is the one to watch

Analysis by BBC North America correspondent Anthony Zurcher

Special counsel Robert Mueller has brought charges against 19 individuals and he has obtained five guilty pleas. Now, with Alex van der Zwaan’s 30-day prison sentence, he has closed his first case.

The lawyer’s ordeal appears somewhat tangential to the central thrust of Mr Mueller’s investigation, but the special counsel’s office made clear that lying to government investigators must have consequences.

In addition, information prosecutors obtained from him may have been key to securing the co-operation of former Trump campaign and transition aide Rick Gates, who could in turn help seal former Trump campaign chair Paul Manafort’s legal fate.

For the moment, at least, Mr Manafort continues to be the central figure in this investigation. Based on information released by Mr Mueller’s office on Monday night, his ties to Russia – while he was involved with the Trump campaign – are squarely under the microscope.

While Van der Zwaan’s sentencing is a milestone in Mr Mueller’s inquiry, Paul Manafort is the biggest and most important domino currently standing.

Who else has been charged by Mr Mueller?

Nineteen people – including Mr Manafort and Mr Gates – have been indicted by the special counsel:

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